🥞 CFD Prism Layer Growth & Inflation Mesh Calculator
Dimension boundary layer prism/inflation layers: compute cumulative thickness $H_{tot}$, layer count $N$, last cell height $h_N$, and transition ratio to the outer volume mesh.
🧱 2D Boundary Layer Prism Mesh Visualization
True-to-Scale Layer Inflation • Bulk Mesh Interface📝 Inflation Parameters
Geometric Progression Equations:
$$h_i = h_1 \cdot r^{i-1} \quad (i = 1, \dots, N)$$ $$H_{tot} = \sum_{i=1}^N h_i = h_1 \frac{r^N - 1}{r - 1}$$ $$R_{trans} = \frac{h_N}{\Delta x_{bulk}} \quad (\text{Target: } 0.7 \le R_{trans} \le 1.3)$$
$$h_i = h_1 \cdot r^{i-1} \quad (i = 1, \dots, N)$$ $$H_{tot} = \sum_{i=1}^N h_i = h_1 \frac{r^N - 1}{r - 1}$$ $$R_{trans} = \frac{h_N}{\Delta x_{bulk}} \quad (\text{Target: } 0.7 \le R_{trans} \le 1.3)$$
📊 Mesh Sizing Results
Boundary Layer Inflation Summary
Total Inflation Height ($H_{tot}$) across 18 Layers
3.9601 mm
= 3.9601e-3 m | First layer $h_1 = 25\ \mu\text{m}$ | Last layer $h_N = 0.7346\ \text{mm}$
Transition Diagnostic: WARNING: Severe step change! Last prism is too small vs bulk mesh (<0.4). (Ratio $h_N / \Delta x_{bulk} = \mathbf{0.245}$)
First Layer ($h_1$)25 μm
Growth Ratio ($r$)1.22
Layer Count ($N$)18
Last Layer ($h_N$)0.735 mm
Bulk Mesh ($\Delta x$)3 mm
Transition Ratio0.245
📈 Layer Thickness $h_i$ [mm]
📊 Cumulative Inflation Height $Y_i$ [mm]
📋 Detailed Layer-by-Layer Progression
| Layer # | Thickness [mm] | Thickness [μm] | Cumulative [mm] | Ratio |
|---|---|---|---|---|
| 1 | 0.025 | 25 | 0.025 | 1 |
| 2 | 0.0305 | 30.5 | 0.0555 | 1.22 |
| 3 | 0.03721 | 37.21 | 0.09271 | 1.22 |
| 4 | 0.0454 | 45.4 | 0.1381 | 1.22 |
| 5 | 0.05538 | 55.38 | 0.1935 | 1.22 |
| 6 | 0.06757 | 67.57 | 0.2611 | 1.22 |
| 7 | 0.08243 | 82.43 | 0.3435 | 1.22 |
| 8 | 0.1006 | 100.6 | 0.4441 | 1.22 |
| 9 | 0.1227 | 122.7 | 0.5668 | 1.22 |
| 10 | 0.1497 | 149.7 | 0.7164 | 1.22 |
| 11 | 0.1826 | 182.6 | 0.8991 | 1.22 |
| 12 | 0.2228 | 222.8 | 1.122 | 1.22 |
| 13 | 0.2718 | 271.8 | 1.394 | 1.22 |
| 14 | 0.3316 | 331.6 | 1.725 | 1.22 |
| 15 | 0.4046 | 404.6 | 2.13 | 1.22 |
| 16 | 0.4936 | 493.6 | 2.623 | 1.22 |
| 17 | 0.6021 | 602.1 | 3.226 | 1.22 |
| 18 | 0.7346 | 734.6 | 3.96 | 1.22 |
Fortran Solver Raw Output:
=============================================================== THERMOFLUIDCALC — CFD PRISM LAYER INFLATION SOLVER =============================================================== Calculation Mode = 1 First Layer h1 [m] = 2.500000E-05 First Layer h1 [mm] = 2.500000E-02 First Layer h1 [um] = 2.500000E+01 Growth Ratio (r) = 1.2200 Number of Layers (N)= 18 Total Height H [m] = 3.960113E-03 Total Height H [mm] = 3.960113E+00 Last Layer h_N [m] = 7.346105E-04 Last Layer h_N [mm] = 7.346105E-01 Bulk Cell Size [m] = 3.000000E-03 Transition Ratio = 2.448702E-01 --------------------------------------------------------------- Transition Diagnostic: WARNING: Severe step change! Last prism is too small vs bulk mesh (<0.4). =============================================================== --- PRISM LAYER DISTRIBUTION --- Layer Thickness[m] Thickness[mm] Cumulative[m] Cumulative[mm] Ratio 1 2.500000E-05 2.500000E-02 2.500000E-05 2.500000E-02 1.0000 2 3.050000E-05 3.050000E-02 5.550000E-05 5.550000E-02 1.2200 3 3.721000E-05 3.721000E-02 9.271000E-05 9.271000E-02 1.2200 4 4.539620E-05 4.539620E-02 1.381062E-04 1.381062E-01 1.2200 5 5.538336E-05 5.538336E-02 1.934896E-04 1.934896E-01 1.2200 6 6.756770E-05 6.756770E-02 2.610573E-04 2.610573E-01 1.2200 7 8.243260E-05 8.243260E-02 3.434899E-04 3.434899E-01 1.2200 8 1.005678E-04 1.005678E-01 4.440576E-04 4.440576E-01 1.2200 9 1.226927E-04 1.226927E-01 5.667503E-04 5.667503E-01 1.2200 10 1.496851E-04 1.496851E-01 7.164354E-04 7.164354E-01 1.2200 11 1.826158E-04 1.826158E-01 8.990512E-04 8.990512E-01 1.2200 12 2.227913E-04 2.227913E-01 1.121842E-03 1.121842E+00 1.2200 13 2.718053E-04 2.718053E-01 1.393648E-03 1.393648E+00 1.2200 14 3.316025E-04 3.316025E-01 1.725250E-03 1.725250E+00 1.2200 15 4.045551E-04 4.045551E-01 2.129805E-03 2.129805E+00 1.2200 16 4.935572E-04 4.935572E-01 2.623363E-03 2.623363E+00 1.2200 17 6.021398E-04 6.021398E-01 3.225502E-03 3.225502E+00 1.2200 18 7.346105E-04 7.346105E-01 3.960113E-03 3.960113E+00 1.2200 --- END PRISM DISTRIBUTION ---